Well the title says it all.
I was wondering how the theme of the video relates to the song.
It is an established and significant part of European theatrical tradition, particularly in Catholic where countries where women were not permitted to perform on stage until the late 1700s. The female parts in Shakespeare's and Marlowe's plays and in opera were played by men. This tradition survives today in its loosest sense as the pantomime dame.
In Britain, this practise continued in the early 20th Century with Alastair Simms, in the St Trinian films, and Arthur Lucan, as Old Mother Riley, respectively.
At the time of the Queen's formation in the late 1960s/early 1970s it was still common to see acts on British television such as Dick Emery, Danny La Rue, Les Dawson and Monty Python appear 'drag-up'.
Similar acts would appear on the BBC 1970s nostalgia show "The Good Old Days" which reprised Victorian era music hall acts.
Queen merely kept a tradition going, with exaggerated comic effect, by parodying a well known, to UK viewers, soap opera.
The song itself is about a break-up of a relationship, written by the bassist, John Deacon, himself married with several children.
The video has very little to do with the lyrics of the song. The video could easily replace the first half of the video for Radio Ga Ga or for A Kind of Magic; Hammer To Fall less so.
The video is best seen as just the four lads larking about, a little like the Beatles in The Magical Mystery Tour.
On the official Queen website, under the entry for The Works is the following quotation from the drummer, Roger Taylor:
"We had done some really serious, epic videos in the past, and we just wanted people to know that we didn't take ourselves too seriously, that we could still laugh at ourselves. I think we proved that."
They parodied the long-running ITV soap opera Coronation Street. The second part of the video included a composition rehearsed and performed with the Royal Ballet and choreographed by Wayne Eagling.
Maybe it’s because the title, “I Want to Break Free”. They could be dressing as drags because they “Broke Free”? Just a theory. Showing that men and women have rights, freedom. Just a thought, I know it doesn’t have much to do with the song, but that’s what they could be using in context to the video. I’m probably wrong but whatever.